Stability of long circular tunnels in sloping ground

Assessment of tunnel stability has become increasingly crucial as more and more tunnels are built in difficult terrains such as sloping ground. The required support pressure on the tunnel walls associates both tunnel stability and liner design considerations. The present analysis attempts to find a uniform internal pressure which can support a circular tunnel built in a sloping ground with a particular level of stability in cohesive-frictional soils. The lower bound finite element limit analysis has been applied to find the required minimum uniform internal support pressure presented as a non-dimensional term p/c; where p is the minimum normal internal pressure on the tunnel boundary to avoid collapse and c is the cohesion of soil. The variation of p/c is presented for a range of normalised embedment depth of tunnel (H/D), stability number (γD/c), internal friction angle of soil (?) and slope angle (β); where H is the crown depth of the tunnel, D is the tunnel diameter and γ is the unit weight of soil. Appropriate comparisons have been carried out with available literature. Failure patterns of the tunnel have also been studied to understand the extent and the type of failure zone which may generate during the collapse.     

Three-dimensional stability analysis of a longitudinally inclined shallow tunnel face

The tunnel inclination angle (δ) generally exists in urban and cross-river (sea) tunnels; hence, its effect should be considered in the stability analysis of a tunnel face. However, the influence of this tunnel inclination angle is rarely studied. In this paper, considering the effects of the tunnel inclination angle and the tunneling length (L), the optimal upper-bound solutions of the active and passive failure pressures were obtained using sequential quadratic programming (SQP) based on the upper-bound limit analysis. The effects of the dimensionless parameters on the pressures and failure modes were investigated. The results show that the tunnel inclination angle δ and the dimensionless parameter L/D (D is the section diameter of the tunnel) significantly affect active and passive stabilities. The difference in the results between δ = −10° and δ = 10° is mostly greater than 10% and reaches 80% when the internal friction angle (φ) is large. When the value of δ is zero, L/D does not affect on the result. The maximum difference in the results between L/D = 0 and L/D = 5 are 92.5% (passive failure) and 36.3% (active failure). For the active failure mode, with increasing of φ, the curves, which have δ values of −10°, 0° and 10°, intersect at a particular point when φ reaches a specific value.     

Face stability analysis of shallow shield tunnels in dry sandy ground using the discrete element method

Controlling the face stability of shallow shield tunnels is difficult due to the inadequate understanding of face failure mechanism. The failure mechanism and the limit support pressure of a tunnel face in dry sandy ground were investigated by using discrete element method (DEM), which has particular advantages for revealing mechanical properties of granular materials. The contact parameters of the dry sand particles were obtained by calibrating the results of laboratory direct shear tests. A series of three-dimensional DEM models for different ratios of the cover depth to the diameter of the tunnel (C/D = 0.5, 1, and 2; i.e., relative depth) were then built to simulated the process of tunnel face failure. The limit support pressure, failure zone and soil arching were discussed and compared with other methods. The results of DEM simulations show that the process of tunnel face failure can be divided into two stages. With the increase of the horizontal displacement of the tunnel face, the support pressure decreases to the limit support pressure and then increases to the residual support pressure. The limit support pressure increases with the rise of relative depth and then tends to be constant. In the process of tunnel face failure, the failure zone is gradually enlarged in size and expands to the ground surface. The numerical results also demonstrate that soil arching occurs in the upper part of the failure zone and the soil becomes loosened in the failure zone. Consequently, the comprehensive analysis of tunnel face failure may help to guarantee safe construction during tunneling.     

A discrete numerical approach for modeling face stability in slurry shield tunnelling in soft soils

In this paper, a numerical simulation method for evaluating tunnelling-induced ground movement is presented. The method involves discrete element simulation of TBM slurry shield advancement and considers explicitly soil excavation from the face, effects of varying face support pressure, and the influence of tunnel cover depth. For the cases studied, it is found that for tunnel cover depths (C/D) between 0.7 and 2.1, ground deformations inducing by the tunnelling can be controlled within a certain extent and tunnel face stability can ensured, provided the support pressure ratio (N) lies between 0.8 and 1.5. The proposed method is reasonably benefited to modeling the face stability in shield-driven tunnels in soft soils.     

Upper bound analysis of tunnel face stability in layered soils

The working face of tunnel constructions has to be kept stable during tunneling to prevent large soil deformations or fatal failure. In layered soils with lower cohesion, failures happen more often and more abrupt than in cohesive soils. Therefore, the maintenance of a proper support pressure at the tunnel working face is of high importance. In this paper, an upper bound analysis is introduced to investigate the minimum support pressure for the face stability in layered soils. A three-dimensional kinematically admissible mechanism for the upper bound analysis is improved to model potential failure within different soil layers. An analytical solution for the support pressure assessment is achieved. The influence of the crossing and cover soil on the face stability is analyzed, respectively. This solution provides an analytical estimation of the minimum support pressure for the face stability. It may be used as a reference for projects under similar conditions.     

Face stability analysis of shield-driven tunnels shallowly buried in dry sand using 1-g large-scale model tests

This paper investigates the face stability of shield-driven tunnels shallowly buried in dry sand using 1-g large-scale model tests. A half-circular tunnel model with a rigid front face was designed and tested. The ground movement was mobilized by pulling the tunnel face backwards at different speeds. The support pressure at tunnel face, settlement at ground surface, and internal movement of soil body were measured by load cells, linear variable differential transducers, and a camera, respectively, and the progress of face failure was observed through a transparent lateral wall of model tank. The tests show that, as the tunnel face moves backwards, the support pressure at the tunnel face drops sharply initially, then rebounds slightly, and tends to be stabilized at the end. Similarly, the ground surface settlement shows a three-stage variation pattern. Using the particle image velocimetry technique, the particle movement, shear strain, and vortex location of soil are analyzed. The variation of support pressure and ground surface settlement related to the internal movement of soil particles is discussed. The impact of the tunnel face moving speed on the face stability is discussed. As the tunnel face moves relatively fast, soil failure originates from a height above tunnel invert and an analytical model is developed to analyze such failure.     

粉砂地层盾构隧道开挖面稳定性离心试验及数值模拟

通过开展离心模型试验,对干粉砂及饱和粉砂中盾构隧道开挖面的失稳破坏特性和极限支护压力进行了研究。通过远程控制开挖面土体位移,获得了支护压力与开挖面位移间的关系曲线及开挖面达到主动极限平衡状态时的破坏模式。2组干砂离心模型试验结果表明,当隧道埋深与隧道直径比从0.5增大到1时,开挖面破坏模式从整体坍塌破坏转变为烟囱状,但极限支护压力变化较小。饱和砂土中的试验表明,开挖面水平方向破坏范围相比在相同埋深干砂中的范围扩大,极限支护压力显著增加。对开挖面破坏过程进行三维弹塑性有限元数值模拟,获得了开挖面极限支护压力和破坏机制,所得结果与试验吻合较好。进一步通过数值模拟,分析了土体强度参数、隧道埋深及渗流对极限支护压力的影响规律。结果表明,渗流条件下开挖面破坏区域及极限支护压力均大于无渗流情况,极限支护压力随内摩擦角增大而减小,随隧道埋深增大而减小。     

黏土地层盾构隧道临界注浆压力计算及影响因素分析

合理选择注浆压力是确保盾构隧道壁后注浆效果良好的前提。假定在黏土地层中,壁后注浆先对周围土体产生压密效应,当注浆压力超过一定值以后,浆液开始劈裂土体。为得到最优注浆压力,基于弹塑性理论,推导了考虑浆体无限扩张时的注浆压力上临界值计算式;将接头螺栓的抗剪效应与注浆对管片产生的压力结合起来,推导了考虑螺栓剪切破坏的注浆压力上临界值计算式;基于主、被动土压力公式,提出了保持地层稳定的注浆压力上、下临界值计算式。在此基础上,提出了最优注浆压力计算方法。通过工程实例,分析了土体的弹性模量、黏聚力、内摩擦角、初始地下水压,及隧道埋深对临界注浆压力的影响。结果表明：临界注浆压力与土体弹性模量、黏聚力、内摩擦角、初始地下水压,管片结构性能以及隧道埋深等因素有关;上临界值随着土体弹性模量、黏聚力、内摩擦角、初始地下水压及隧道埋深的增大而增大;下临界值亦随隧道埋深的增大而增大。     

砂卵石地层土压盾构掘进掌子面稳定性室内试验与三维离散元仿真研究

采用?800 mm模型土压盾构开展室内掘进试验,以探究砂卵石中土压盾构隧道掌子面失稳诱发地层变形特征。同时,补充开展三维离散元仿真以挖掘室内试验难以获取的掌子面失稳信息,并研究隧道埋深对掌子面稳定性的影响规律。研究结果表明：砂卵石地层中盾构隧道掌子面失稳发展到地表后,沉降曲面呈上大下小逐步收缩的沙漏状,影响范围小于砂土地层。考虑盾构动态掘进过程后,卵石颗粒接触关系变化十分剧烈,掌子面稳定性被削弱,极限支护压力随之增大。掌子面极限支护压力随隧道埋深基本呈线性增加,极限支护压力与初始支护压力之比则随埋深增大而减小。掌子面失稳机制可根据隧道埋深划分为3种模式。与既有研究相比,考虑了盾构动态掘进过程与实际工程更加接近,可为确保砂卵石地层土压盾构隧道施工掌子面稳定提供参考。     

Discrete element modeling of static liquefaction of shield tunnel face in saturated sand

The failure mechanism and limit support pressure are essential factors for the stability assessment of tunnel face during shield tunneling. Previous studies were mostly based on the assumption that soil fails when the plastic limit is reached. The static liquefaction of saturated sand at pre-failure state often largely reduces shear strength; a stable tunnel face could be destabilized and even collapses abruptly. This paper aims to explore the static liquefaction failure of tunnel face in saturated sands by 3D discrete element simulation. The particle shape is considered by using clump composed of two identical spheres, and the micro-material parameters are calibrated by fitting against triaxial tests. The tunnel face is initially supported by the earth pressure at rest, and then the pressure is reduced by applying a displacement on the free surface until soil body completely collapses. The second-order work during the unloading process is calculated, and a negative value denotes the initiation of static liquefaction. The distribution of negative second-order work point shows the initiation and propagation of static liquefaction. The ultimate failure mode is shown to be composed of a sliding wedge and an overlying chimney, and the chimney is confined to a local area for soil arching. The experienced stress path of tunnel face verifies the existence of static liquefaction instability, indicating the stability analysis should consider static liquefaction rather than simply using the conventional plastic limit state analysis.

     

Contours of saturated and unsaturated overhanging slopes at limiting equilibrium condition

Overhangs are frequently observed in riverbanks, coastal headlands, and rock formations. The geometry of an overhang is an input into most slope stability analyses and is often idealised or back-calculated from empirical data. This study investigates the geometries of overhang slopes, which exist while in limiting conditions satisfying static equilibrium with soil strength governed by the Mohr-Coulomb failure criterion. The overhanging contour is formulated as the unknown in a boundary value problem and solved for using the slip line theory. Analyses consider nonhomogeneous soils, where cohesion and, if unsaturated, the contribution of suction to the effective stress vary linearly with depth. The solutions are presented in general dimensionless charts. Applications of the charts are illustrated via examples. It has been observed that soil with varying amounts of friction and cohesion could develop overhanging arches of different sizes and shapes. This study shows that the curvature of an overhang becomes more pronounced for small values of φ′ . It is also demonstrated that changing the contribution of suction to the effective stress has a direct impact on the size of an unsaturated soil overhang. Overhanging slope shapes observed in reality may be different from the idealised subset studied in this paper since real slopes are not necessarily at impending failure. The real shapes may be influenced by various physical processes such as weathering, stress variations caused by cycles of wetting-drying. Even so, the results presented in the paper indicated how key soil properties influence slope shapes, albeit it while in limiting conditions.     

非均质黏土地基中平面应变隧道最小支护压力数值模拟

土体由于沉积而具有天然的非均质性,但关于非均质地基中隧道开挖面稳定性的研究却很稀少,在实际盾构隧道工程中均按均质地基对待。但这一简化并没有考虑非均质性对保持开挖面稳定所需最小支护压力的有利作用,以及对破坏模式的影响。故文中采用基于tresca准则的弹塑性有限元法来研究黏聚力随深度线性变化的纯黏土地基中平面应变隧道的开挖面稳定性,模拟了土体失稳渐进破坏的全过程。最终验证了无量纲化的有效性,得到了各种工况时保持土体稳定的最小支护压力值,并发现了黏聚力线性变化斜率对深埋隧道破坏模式的影响,可为理论分析和工程实践提供依据。     

坑中坑条件下基坑有限土体的被动土压力计算

坑中坑在基坑工程实践中普遍存在,使得基坑底部土体成为有限土体,因此,常规的建立在半无限空间土体假定上的朗肯土压力理论对于坑中坑条件下的基坑不再适用。基于极限平衡理论和平面滑裂面假定,考虑土体黏聚力和滑动土体不同的形状,推导了4种情况下被动土压力的计算公式,并给出了滑裂面剪切破坏角的数学表达式。通过算例,计算了不同内坑位置条件下被动土压力的大小和变化趋势。结果表明,滑裂面剪切破坏角是与土体内摩擦角、黏聚力、计算深度、内坑大小及位置有关的变量,内坑的存在将降低围护结构上的被动土压力,且存在一个内坑影响最不利位置,此时的被动土压力值最小。成果为基坑围护设计中被动土压力的计算提供了理论基础。     

Probabilistic evaluation of tunnel face stability in spatially random soils using sparse polynomial chaos expansion with global sensitivity analysis

The sparse polynomial chaos expansion is employed to perform a probabilistic analysis of the tunnel face stability in the spatially random soils. A shield tunnel under compressed air is considered which implies that the applied pressure is uniformly distributed on the tunnel face. Two sets of failure mechanisms in the context of the limit analysis theory with respect to the frictional and the purely cohesive soils are used to calculate the required face pressure. In the case of the frictional soils, the cohesion and the friction angle are modeled as two anisotropic cross-correlated lognormal random fields; for the purely cohesive soils, the cohesion and the unit weight are modeled as two anisotropic independent lognormal random fields. The influences of the spatial variability and of the cross-correlation between the cohesion and the friction angle on the probability density function of the required face pressure, on the sensitivity index and on the failure probability are discussed. The obtained results show that the spatial variability has an important influence on the probability density function as well as the failure probability, but it has a negligible impact on the Sobol’s index.     

Pseudo-dynamic evaluation of passive response on the back of a retaining wall supporting c-Φ backfill

The study presents a rational analytical approach to obtain the seismic passive response of an inclined retaining wall backfilled with horizontal c-Φ soil. Pseudo-dynamic analysis is carried out to obtain the seismic passive response. Here in this analysis, the critical wedge angle is a single one irrespective of weight, surcharge and cohesion and this fact satisfies the field situation in a more realistic manner. A planer failure surface is considered in the analysis. The effect of soil and wall friction angle, wall inclination, horizontal and vertical earthquake acceleration on the passive resistance and the variation of passive earth pressure along the height of the wall have been explored. A comparison to pseudo-static and other available methods have been made to highlight the non-linearity of seismic passive earth pressure distribution.     

深埋盾构隧道开挖面三维对数螺旋破坏模式的上限分析

相对于盾构隧道施工的大量需求与快速发展的状况,国内在盾构工法特别是大型深埋盾构隧道施工技术和理论研究方面还存在不足,特别是水压条件下深埋盾构隧道开挖面稳定问题。基于极限分析上限法和水土压力统一参数,对考虑水压影响的均质土深埋隧道开挖面稳定性计算方法进行研究,建立了考虑水压影响的深埋盾构隧道开挖面三维对数螺旋破坏模式模型,并推导了其极限支护压力计算公式。然后利用土层厚度加权平均法,可将上述方法应用于多层土深埋盾构隧道开挖面稳定性的评价中。最后,以上海长江盾构隧道实际工程为例,采用本文推导的极限分析上限三维对数螺旋破坏模式方法计算并分析其极限支护压力,并将计算结果与前人研究和规范方法计算的结果进行对比分析。通过该研究可改进与完善水压条件下深埋盾构隧道极限支护压力确定方法,从而为考虑水压条件下盾构隧道施工支护压力的合理确定提供理论依据。     

Uncertainty of rainfall-induced landslides considering spatial variability of parameters

A cross-correlation analysis is conducted to determine the impacts of the heterogeneity of hydraulic conductivity K_s, soil cohesion c′ and soil friction angle (tan φ′) on the uncertainty of slope stability in time and space during rainfall. We find the relative importance of tan φ′ and c′ depends on the effective stress. While the sensitivity of the stability to the variability of K_s is small, the large coefficient of variation of K_s may exacerbate the variability of pore-water pressure. Therefore, characterizing the heterogeneity of hydraulic properties and pore-water distribution in the field is critical to the stability analysis.     

Probabilistic analysis of three-dimensional tunnel face stability in soft rock masses using Hoek–Brown failure criterion

This paper investigates tunnel face stability in soft rock masses via coupled limit and reliability analyses. Specifically, a 3D face collapse mechanism was first constructed. Then the Hoek–Brown failure criterion was introduced into the limit analysis via the tangential technique. Taking the variability of rock mass parameters and loads into consideration, a reliability model was established. The collapse pressure and failure range of tunnel faces were determined. In addition, the required factor of safety (FS) and supporting pressure under three safety levels were obtained, and the corresponding safety level graphs for support design were presented. Comparison of the obtained results with previous work demonstrates the rationality of the 3D collapse mechanism and the validity of the results. A decrease in the geological strength index, Hoek–Brown parameter m_i, and uniaxial compressive strength or an increase in the disturbance factor results in a nonlinear increase of the collapse pressure and an enlargement of the failure zone. Such changes also lead to a nonlinear increase of the required support pressure under a certain safety level. By contrast, the FS does not exhibit any obvious change when these parameters vary. Therefore, when a rock mass is of poor quality or heavily disturbed, the advance support should be enlarged from upper front to right above the tunnel face. Moreover, as the safety level increases, both the required FS and supporting pressure of the tunnel face increase nonlinearly at a higher rate.     

The effect of pore water pressure on tunnel face stability

The kinematic approach in combination with numerical simulation is used to examine the effect of pore water pressure on tunnel face stability. Pore water pressure distribution obtained by numerical calculations using FLAC^3D is used to interpolate the pore water pressure on a 3D rotational collapse mechanism. Comparisons are made to check the present approach against other solutions, showing that the present approach improves the existing upper bound solutions. Results obtained indicate that critical effective face pressure increases with water table elevation. Several normalized charts are also presented for quick evaluation of tunnel face stability. At the end of the paper, the influence of anisotropic permeability on tunnel face stability is also discussed, showing that the isotropic model leads to an overestimation of the necessary tunnel face pressure for anisotropic soils. Copyright © 2016 John Wiley & Sons, Ltd.     

地表超载作用下隧道失稳破坏的上限有限元分析

针对地表超载作用下隧道稳定性和破坏模式问题,基于刚体平动运动单元上限有限元理论编程并计算分析,获得了浅埋隧道失稳临界超载系数上限解和刚性运动块体体系破坏模式。通过与现有的刚性块体极限分析上限法以及极限分析上、下限有限元法计算结果的对比分析,验证了上限解的可靠性。研究结果表明,（1）临界超载系数 黏聚力c之比 随土体内摩擦角 和隧道埋深C与直径D之比( )的增大而相应增大,随土体重度与黏聚力参数 的增大而减小;（2） 和 对隧道破坏模式的影响较明显; 增大,则隧道破坏范围增加;内摩擦角 增大,刚性运动块体破坏模式相互错动更加显著,相比而言, 对破坏模式的影响并不显著;（3）刚体平动运动单元上限有限元上限解精度高,所得刚性运动块体破坏模式具有滑移线形态,能精细地反映隧道失稳破坏特征。